IB Physics D1 Notes

In Topic B.5, you learned that electric fields have a potential difference. The same applies to any other field, including gravitational fields. Thus, gravitational potential (V_g) is the energy per unit test point mass, measured in J kg^-1. Newton’s law of universal gravitation provides a formula for the gravitational potential at a distance (r) from any point mass (M):

$V_{g} = \frac{-GM}{r}$

Remember that when a test point is moved:

1. Parallel to field lines - the test point mass is moving in the direction of the force. Therefore, work is done on the object.
2. Perpendicular to field lines - the test point mass is not moving in the direction of the force. Therefore, no work is done on the object.

When work is done moving a test point mass between two locations, the energy is transferred into changing its potential. Therefore, there is a gravitational potential difference (ΔV) between the two locations. The gravitational potential difference (ΔV_g) is defined as the work done moving a test point mass per unit test point mass, measured in J kg^-1.

If work is done on the test point mass to change its potential, the potential difference will be positive. If the test point mass does work itself to change its potential, the potential difference will be negative. The formula for this is:

$W = m\Delta V_{g}$